A device of this type is disclosed in EP-B1-0 258 450. In this device, a beam is focused by a focusing means onto an optical recording medium at a focal point. The focal point is guided along data tracks of the recording medium by a displacement means which displaces the position of the focal point on the recording medium. The position of the focal point on the recording medium is displaced by the displacement means indirectly in this device, that is to say by way of the displacement of a lens of the focusing means, which results in displacement of the position of the focal point on the recording medium. The direction of movement is in this case perpendicular to the direction of the tracks present on the recording medium, the focal point being moved both in the positive direction and in the negative direction, depending on the requirement, while the tracks move away under the focal point in their longitudinal direction on account of the rotary movement of the recording medium. Due to inaccuracies, for example in the eccentricity of the recording medium designed as a disk, for example a CD, and tolerances in the securing of the recording medium in the device, it is necessary to displace the focal point virtually at all times in order to keep it on the track. In order to achieve a higher data transfer rate, it is expedient to increase the reading speed of the device. The consequence of this is that the displacements of the focal point on the recording medium which are necessary for the purpose of tracking have to be effected at an increased frequency. The known device may be regarded as having the disadvantage that it is unable, owing to the inertia of the focusing means, to achieve a desired high data transfer rate since tracking of the focal point on a track of the recording medium is no longer ensured correctly at a high reading speed.